Which of the following cations has the strongest tendency towards complex formation?

Options

A. `Sm^(3+)`
B. `Lu^(3+)`
C. `Gd^(3+)`
D. `Yb^(3+)`

Answer

To determine which of the given cations has the strongest tendency towards complex formation, we will analyze the properties of the lanthanide cations mentioned: Samarium (Sm³⁺), Gadolinium (Gd³⁺), Ytterbium (Yb³⁺), and Lutetium (Lu³⁺).

### Step 1: Identify the Cations
The cations we are considering are:
- Samarium (Sm³⁺)
- Gadolinium (Gd³⁺)
- Ytterbium (Yb³⁺)
- Lutetium (Lu³⁺)

### Step 2: Understand the Concept of Complex Formation
Complex formation involves the interaction between metal cations and ligands. The tendency of a metal ion to form complexes is influenced by its charge density, which is a function of its size and charge.

### Step 3: Analyze the Size of the Cations
- Lanthanide ions generally decrease in size as we move from left to right in the periodic table due to the increasing nuclear charge, which pulls the electrons closer to the nucleus.
- The ionic radii of the cations decrease from Samarium to Lutetium.

### Step 4: Compare the Ionic Sizes
- Samarium (Sm³⁺): Larger ionic radius
- Gadolinium (Gd³⁺): Intermediate ionic radius
- Ytterbium (Yb³⁺): Smaller than Gd³⁺ but larger than Lu³⁺
- Lutetium (Lu³⁺): Smallest ionic radius among the given cations

### Step 5: Determine Charge Density
The charge density is calculated as the charge of the ion divided by its volume (related to the ionic radius). A smaller ionic radius with the same charge means a higher charge density.

- Lutetium (Lu³⁺) has the smallest size, which means it has the highest charge density.

### Step 6: Conclusion
Since Lutetium (Lu³⁺) has the smallest ionic radius and thus the highest charge density, it will have the strongest tendency to attract ligands and form complexes. Therefore, Lutetium (Lu³⁺) is the cation with the strongest tendency towards complex formation.

### Final Answer
The cation with the strongest tendency towards complex formation is **Lutetium (Lu³⁺)**.

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