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 hydroxides (cerium hydroxide, lutetium hydroxide, yttrium hydroxide, and promethium hydroxide), we can follow these steps:

### Step 1: Identify the Elements
The elements in question are cerium (Ce), lutetium (Lu), yttrium (Y), and promethium (Pm). All of these elements belong to the lanthanide series.

### Step 2: Understand Lanthanide Contraction
As we move from lanthanum (La) to lutetium (Lu) in the lanthanide series, there is a phenomenon known as lanthanide contraction. This is due to the poor shielding effect of the f-orbitals, which leads to a decrease in the size of the cations as the atomic number increases.

### Step 3: Analyze Cation Sizes
The cations formed from these hydroxides are:
- Cerium (Ce³⁺)
- Promethium (Pm³⁺)
- Yttrium (Y³⁺)
- Lutetium (Lu³⁺)

Due to lanthanide contraction, cerium (Ce³⁺) is the largest cation among these four.

### Step 4: Apply Fajan's Rule
According to Fajan's rule, the smaller the size of the cation, the greater the covalent character of the bond. Conversely, larger cations have a greater ionic character. Since we are looking for the strongest base, we need to find the hydroxide with the greatest ionic character, which corresponds to the largest cation.

### Step 5: Determine Basicity
The basicity of a hydroxide is related to its tendency to release hydroxide ions (OH⁻). The larger the cation, the more ionic character it has, which means it will more readily dissociate to release hydroxide ions.

### Step 6: Conclusion
Since cerium (Ce³⁺) is the largest cation among the options, it will have the highest ionic character and, therefore, cerium hydroxide (Ce(OH)₃) will be the strongest base among the given options.

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

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