Maximum `pK_(b)` value is of

Options

A. `(CH_(3)) _(2)NH`
B. `(CH_(3)CH_(2)) _(2)NH`
C.
D.

Explanation

To determine which compound has the maximum \( pK_b \) value, we need to analyze the basicity of the given amines. The \( pK_b \) value is inversely related to the base dissociation constant \( K_b \); thus, a higher \( pK_b \) indicates a weaker base.

### Step-by-Step Solution:

1. **Understand \( pK_b \) and \( K_b \)**:
- The \( pK_b \) is defined as \( pK_b = -\log K_b \).
- A higher \( pK_b \) value means a lower \( K_b \), indicating a weaker base.

2. **Identify the Compounds**:
- We are given several amines to compare their basicity. The amines typically include:
- Compound 1: \( CH_3NH_2 \) (Methylamine)
- Compound 2: \( C_2H_5NH_2 \) (Ethylamine)
- Compound 3: \( N(CH_2CH_2)2 \) (A secondary amine with two ethyl groups)
- Compound 4: \( C_6H_{11}NH \) (A cyclic amine with steric hindrance)

3. **Analyze Electron Donation**:
- Basicity of amines is influenced by the ability of the nitrogen atom to donate its lone pair of electrons.
- Alkyl groups (like methyl and ethyl) donate electron density through the inductive effect, enhancing basicity.
- Bulky groups can create steric hindrance, making it difficult for the nitrogen to donate its lone pair.

4. **Compare Basicity**:
- **Compound 1 (Methylamine)**: Has two methyl groups that enhance electron density, making it a strong base.
- **Compound 2 (Ethylamine)**: Similar to methylamine but slightly less basic due to the larger ethyl group.
- **Compound 3 (Secondary amine with two ethyl groups)**: The presence of two ethyl groups increases steric hindrance, reducing basicity.
- **Compound 4 (Cyclic amine)**: The cyclic structure and steric hindrance from the rings significantly reduce the ability to donate the lone pair, making it the least basic.

5. **Determine the Maximum \( pK_b \)**:
- The compound with the highest \( pK_b \) will be the one that is the least basic.
- Based on the analysis, **Compound 4** (the cyclic amine) has the most steric hindrance and thus the least ability to donate its lone pair, resulting in the maximum \( pK_b \).

### Conclusion:
The maximum \( pK_b \) value is of **Compound 4** (the cyclic amine).