Which out of the two ,`La(OH)_(3) and Lu(OH)_(3)`, is more basic and why?

Answer

To determine which of the two hydroxides, La(OH)₃ (lanthanum hydroxide) or Lu(OH)₃ (lutetium hydroxide), is more basic, we need to analyze their properties based on the lanthanoid series.

### Step-by-Step Solution:

1. **Understanding the Lanthanoid Series**:
- The lanthanoid series consists of elements from lanthanum (La) to lutetium (Lu). As we move from La to Lu, the atomic number increases, and the size of the ions decreases due to a phenomenon known as lanthanoid contraction.

**Hint**: Remember that lanthanoid contraction refers to the gradual decrease in ionic size across the series.

2. **Ionic Size and Basicity**:
- As we move across the lanthanoid series, the ionic size decreases. Smaller ions have a higher charge density, which leads to a stronger attraction for electrons.

**Hint**: Consider how ionic size affects the ability of an ion to donate or accept electrons.

3. **Basic Nature of Hydroxides**:
- Basicity is related to the ability of a compound to donate electrons. Larger ions tend to have a greater ability to donate electrons, while smaller ions with higher nuclear charge tend to attract electrons more strongly.

**Hint**: Think about the Lewis theory of acids and bases, where electron donors are bases and electron acceptors are acids.

4. **Comparison of La(OH)₃ and Lu(OH)₃**:
- La(OH)₃ has a larger ionic size compared to Lu(OH)₃. This means that La³⁺ will have a lower nuclear pull compared to Lu³⁺, making it easier for La(OH)₃ to donate electrons.

**Hint**: Recall that larger ionic size generally correlates with higher basicity.

5. **Conclusion**:
- Therefore, La(OH)₃ is more basic than Lu(OH)₃ because the larger ionic size of La³⁺ allows it to donate electrons more readily compared to the smaller, more electron-attracting Lu³⁺.

### Final Answer:
La(OH)₃ is more basic than Lu(OH)₃ due to the larger ionic size of La³⁺, which allows it to donate electrons more readily compared to the smaller Lu³⁺.