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Question 147

Among the following acids which has the lowest p$$K_a$$ value

Solution

The acidity order of aliphatic carboxylic acids is governed mainly by the inductive effect ( $$+I$$ effect ) of the alkyl groups attached to the carboxyl carbon.

1. When an acid loses $$H^+$$ it forms the carboxylate ion $$RCOO^-$$.
2. An alkyl group $$R$$ is electron-donating ( $$+I$$ ). It pushes electron density toward the negatively charged $$COO^-$$ group, destabilising it.
3. Greater destabilisation of the anion means lower acid strength, hence higher $$pK_a$$.

Therefore:
• No alkyl group (formic acid, $$HCOOH$$) ⇒ maximum stability of $$HCOO^-$$ ⇒ strongest acid ⇒ lowest $$pK_a$$.
• One methyl group (acetic acid, $$CH_3COOH$$) weakens the acid slightly.
• One ethyl group (propionic acid, $$CH_3CH_2COOH$$) has a stronger $$+I$$ effect than methyl, so the acid is still weaker.
• Two methyl groups $$(CH_3)_2CHCOOH$$ (isobutyric acid) give the largest $$+I$$ effect, making it the weakest acid of the set.

Hence the acidity (and Ka) order is
$$HCOOH \; \gt \; CH_3COOH \; \gt \; CH_3CH_2COOH \; \gt \; (CH_3)_2CHCOOH$$
corresponding to the lowest $$pK_a$$ for formic acid.

Option B which is: HCOOH

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