Question

Arrange the following in increasing order of \(pK_a\) values

• A. \(c \lt b \lt a \lt d\)
• B. \(b \lt d \lt c \lt a\)
• C. \(a \lt d \lt b \lt c\)
• D. \(a \lt b \lt c \lt d\)

Hint:

Electron withdrawing groups increase acidity and decrease \(pK_a\), while electron donating groups decrease acidity and increase \(pK_a\).

Answer 1

The Correct Option is C

Step 1: Understand relation between acidity and \(pK_a\).
Lower \(pK_a\) means stronger acid.
Higher \(pK_a\) means weaker acid.
So, increasing order of \(pK_a\) means: \[ \text{strongest acid} \rightarrow \text{weakest acid} \]

Step 2: Identify the compounds.
Compound \(a\) is \(p\)-nitrobenzoic acid.
Compound \(b\) is \(p\)-methoxybenzoic acid.
Compound \(c\) is \(p\)-nitrophenol.
Compound \(d\) is benzoic acid.

Step 3: Compare acidic strength.
The \(-NO_2\) group is electron withdrawing.
It stabilizes the carboxylate ion and increases acidity.
Therefore, \[ p\text{-nitrobenzoic acid} \] has the lowest \(pK_a\).
So, \[ a \] comes first.
Benzoic acid has no electron donating or withdrawing substituent.
Thus, it is less acidic than \(p\)-nitrobenzoic acid.
So, \[ d \] comes after \(a\).
The \(-OCH_3\) group is electron donating by resonance.
It decreases the acidity of benzoic acid.
So, \[ b \] has higher \(pK_a\) than \(d\).
Phenols are weaker acids than carboxylic acids.
Therefore, \[ p\text{-nitrophenol} \] has the highest \(pK_a\) among these.
So, \[ c \] comes last.

Step 4: Final order.
Hence, the increasing order of \(pK_a\) is: \[ a \lt d \lt b \lt c \]

Step 5: The final conclusion.
Therefore, the correct answer is \[ \boxed{a \lt d \lt b \lt c} \]