Which of the following will have lowest value of `pK_(b)`?

Options

A. `CH_(3)NH_(2)`
B. `(CH_(3))_(2) NH`
C. `NH_(3)`
D. `C_(6)H_(5)NH_(2)`

Explanation

To determine which of the given compounds has the lowest value of \( pK_b \), we need to analyze the basic strength of each compound. The lower the \( pK_b \) value, the stronger the base. Here’s a step-by-step breakdown of how to approach the problem:

### Step 1: Understand the Relationship Between Basicity and \( pK_b \)
- Basicity refers to the ability of a compound to accept protons (H⁺ ions).
- The \( pK_b \) value is a measure of the strength of a base; lower \( pK_b \) indicates a stronger base.

### Step 2: Identify the Compounds
- Let's assume the options are:
1. Methylamine (CH₃NH₂)
2. Dimethylamine (NH(CH₃)₂)
3. Ammonia (NH₃)
4. Aniline (C₆H₅NH₂)

### Step 3: Analyze Each Compound
- **Methylamine (CH₃NH₂)**:
- It has one methyl group which is an electron-donating group. This increases the availability of the lone pair on nitrogen, enhancing basicity.

- **Dimethylamine (NH(CH₃)₂)**:
- It has two methyl groups, which means it has a greater electron-donating effect compared to methylamine. This will further increase the availability of the lone pair on nitrogen, making it a stronger base than methylamine.

- **Ammonia (NH₃)**:
- It has no electron-donating groups. Therefore, it has the least basicity among the three amines mentioned so far.

- **Aniline (C₆H₅NH₂)**:
- The lone pair on nitrogen is involved in resonance with the aromatic ring, which decreases its availability to accept protons. This makes aniline less basic than the aliphatic amines.

### Step 4: Compare Basicities
- Based on the analysis:
- Dimethylamine is the strongest base due to the presence of two electron-donating groups.
- Methylamine is less basic than dimethylamine but more basic than ammonia and aniline.
- Ammonia is less basic than both methylamine and dimethylamine.
- Aniline is the least basic due to resonance stabilization of the lone pair.

### Step 5: Conclusion
- Since dimethylamine has the highest basicity, it will have the lowest \( pK_b \) value among the options given.

### Final Answer
- The compound with the lowest \( pK_b \) value is **Dimethylamine (NH(CH₃)₂)**.

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