Correct Order of Acid Strength for Carboxylic Acids

To determine the relative order of acidic strength among the given carboxylic acids, we evaluate the stability of their corresponding conjugate bases (carboxylate anions), which is influenced by electronic effects such as hybridization, inductive effect ($-I/+I$), and mesomeric effect ($+M/-M$):

1. Compound I ($\text{HC}\equiv\text{C}-\text{COOH}$): The carboxyl group is attached to an $sp$-hybridized carbon atom ($50\%$ $s$-character). Because $sp$-hybridized carbon is highly electronegative, it exerts a strong electron-withdrawing inductive effect ($-I$). This significantly stabilizes the negative charge on the carboxylate anion ($\text{HC}\equiv\text{C}-\text{COO}^-$), making I the most acidic compound ($pK_a \approx 1.84$).

2. Compound II ($\text{H}_2\text{C}=\text{CH}-\text{COOH}$): The carboxyl group is attached to an $sp^2$-hybridized carbon atom ($33.3\%$ $s$-character). An $sp^2$-carbon is more electronegative than an $sp^3$-carbon, so it exerts a moderate $-I$ effect, which stabilizes the conjugate base more effectively than an alkyl group ($pK_a \approx 4.25$).

3. Compound III ($p\text{-MeO}-\text{C}_6\text{H}_4-\text{COOH}$): The methoxy ($-\text{OCH}_3$) group at the para-position exerts a strong electron-donating mesomeric effect ($+M$) into the aromatic ring and towards the carboxylate group. This increases electron density on the carboxyl group and destabilizes the conjugate base, reducing its acidity compared to benzoic acid and acrylic acid ($pK_a \approx 4.47$).

4. Compound IV ($\text{CH}_3\text{CH}_2-\text{COOH}$): The ethyl group is connected via an $sp^3$-hybridized carbon ($25\%$ $s$-character) and exerts an electron-donating inductive effect ($+I$) along with hyperconjugation. This destabilizes the carboxylate anion, making IV the least acidic among the given compounds ($pK_a \approx 4.87$).

Comparing the $pK_a$ values ($\text{lower } pK_a = \text{stronger acid}$): $pK_a(\text{I}) \approx 1.84 < pK_a(\text{II}) \approx 4.25 < pK_a(\text{III}) \approx 4.47 < pK_a(\text{IV}) \approx 4.87$

Thus, the correct order of acidic strength is: $\text{I} > \text{II} > \text{III} > \text{IV}$

Correct Option: B