Question

What is the order of pK$_b$ for the following molecules in an aqueous medium?

• A. P $<$ R $<$ Q $<$ S
• B. P $<$ Q $<$ R $<$ S
• C. S $<$ P $<$ R $<$ Q
• D. S $<$ P $<$ Q $<$ R

Hint:

Basicity: Aliphatic amines $>$ Aromatic amines.
For aromatic amines, adding electron-donating alkyl groups on the nitrogen increases basicity ($\text{p}K_b$ decreases).
Thus, the more methyl groups on aniline, the stronger the base (lower $\text{p}K_b$).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question asks for the correct ascending order of $\text{p}K_b$ values for four amine molecules (P, Q, R, and S) in an aqueous medium.

Step 2: Key Formula or Approach:
Recall the relationship between base strength ($K_b$) and $\text{p}K_b$:
\[ \text{p}K_b = -\log_{10} K_b \] - A stronger base has a higher $K_b$ and a lower $\text{p}K_b$ value.
- A weaker base has a lower $K_b$ and a higher $\text{p}K_b$ value.
Thus, the ascending order of $\text{p}K_b$ will run from the strongest base (lowest $\text{p}K_b$) to the weaker base (highest $\text{p}K_b$).

Step 3: Detailed Explanation:
Let's analyze the factors affecting the basicity of these amines:

• 1. Benzylamine (P):
- In benzylamine ($\text{Ph}-\text{CH}_2-\text{NH}_2$), the nitrogen atom's lone pair is separated from the benzene ring by an $sp^3$ hybridized carbon ($-\text{CH}_2-$).
- Because of this, the lone pair cannot participate in resonance with the aromatic $\pi$-system.
- The lone pair is highly localized and readily available for protonation. This makes P an aliphatic-like amine, which is vastly more basic than any of the aromatic amines (Q, R, and S).
- Therefore, P is the strongest base and has the lowest $\text{pK_b$}.

• 2. Comparing Arlyamines: Aniline (S), N-methylaniline (Q), and N,N-dimethylaniline (R):
- In these three amines, the nitrogen lone pair is directly conjugated with the benzene ring, allowing delocalization and significantly reducing their basicity relative to P.
- To order S, Q, and R, we examine the inductive effect (+I) of the methyl ($-\text{CH}_3$) groups attached to the nitrogen atom.
- Methyl groups are electron-donating groups. They increase the electron density on the nitrogen atom and stabilize the conjugate acid (anilinium ion) formed upon protonation.
- Aniline (S) has no methyl substituents. It is the weakest base among these three.
- N-methylaniline (Q) has one methyl group, which increases its basicity compared to S.
- N,N-dimethylaniline (R) has two electron-donating methyl groups, which further increase its basicity compared to Q.
- Therefore, the basicity order of the aromatic amines is:
\[ \text{S (weakest)} < \text{Q} < \text{R (strongest)} \] - Combining this with the highly basic Benzylamine (P), the overall basicity order in aqueous medium is:
\[ \text{S} < \text{Q} < \text{R} < \text{P} \] - Because $\text{p}K_b$ is inversely proportional to basicity, the order of $\text{p}K_b$ is the exact reverse:
\[ \text{p}K_b(\text{P}) < \text{p}K_b(\text{R}) < \text{p}K_b(\text{Q}) < \text{p}K_b(\text{S}) \]

Step 4: Final Answer:
The ascending order of $\text{p}K_b$ is $\text{P} < \text{R} < \text{Q} < \text{S}$, which corresponds to option (A).