The strongest base is

Options

A. `Ce(OH)_(3)`
B. `Lu(OH)_(3)`
C. `Yb(OH)_(3)`
D. `PM(OH)_(3)`

Answer

To determine the strongest base among the given options, we need to analyze the electron donation ability of each metal hydroxide compound. The stronger the base, the easier it is for the metal to donate electrons.

### Step-by-Step Solution:

1. **Identify the Compounds**: The question provides four metal hydroxides:
- Cerium hydroxide (Ce(OH)₃)
- Lutetium hydroxide (Lu(OH)₃)
- Ytterbium hydroxide (Yb(OH)₃)
- Promethium hydroxide (Pm(OH)₃)

2. **Determine the Oxidation States**: All the given metal hydroxides are in the +3 oxidation state. This means that each metal ion has lost three electrons.

3. **Write Electron Configurations**:
- **Cerium (Ce)**: [Xe] 4f¹ 5d¹ 6s² → In +3 state: [Xe] 4f¹
- **Lutetium (Lu)**: [Xe] 4f¹⁴ 5d¹ 6s² → In +3 state: [Xe] 4f¹⁴
- **Ytterbium (Yb)**: [Xe] 4f¹⁴ 6s² → In +3 state: [Xe] 4f¹³
- **Promethium (Pm)**: [Xe] 4f⁵ 6s² → In +3 state: [Xe] 4f⁴

4. **Analyze Electron Donation**:
- The ability to donate electrons is influenced by the number of electrons in the f-orbital. The more electrons present, the harder it is to lose them.
- **Cerium (Ce)** has 1 electron in the 4f orbital, making it easier to lose this electron.
- **Lutetium (Lu)** has a completely filled 4f orbital (14 electrons), making it difficult to lose electrons.
- **Ytterbium (Yb)** has 13 electrons in the 4f orbital, which is still relatively stable and less likely to lose an electron compared to Cerium.
- **Promethium (Pm)** has 4 electrons in the 4f orbital, which is also more stable than Cerium.

5. **Conclusion**: Since Cerium has the least number of electrons in the f-orbital (1 electron), it can donate electrons most easily, making **Cerium hydroxide (Ce(OH)₃)** the strongest base among the options provided.

### Final Answer:
The strongest base is **Cerium hydroxide (Ce(OH)₃)**.

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