Which one of the following is a hard base ?

Options

A. `Ag^(+)`
B. `Cr^(3+)`
C. `I^(-)`
D. `F^(-)`

Explanation

To determine which of the given options is a hard base, we need to understand the concept of hard and soft acids and bases, as defined by the HSAB (Hard and Soft Acids and Bases) theory.

### Step-by-Step Solution:

1. **Define Hard Bases**:
Hard bases are species that are small in size and have a high charge density. They are less polarizable and typically form strong bonds with hard acids.

2. **Analyze the Options**:
We have four options to consider:
- A. \( \text{Ag}^+ \) (Silver ion)
- B. \( \text{Cr}^{3+} \) (Chromium ion)
- C. \( \text{I}^- \) (Iodide ion)
- D. \( \text{F}^- \) (Fluoride ion)

3. **Evaluate Each Option**:
- **A. \( \text{Ag}^+ \)**: Silver ion is considered a soft acid and does not correspond to a hard base.
- **B. \( \text{Cr}^{3+} \)**: Chromium ion can act as a hard acid, but it is not a base.
- **C. \( \text{I}^- \)**: Iodide ion is larger and more polarizable, making it a soft base.
- **D. \( \text{F}^- \)**: Fluoride ion is small and has a high charge density, making it a hard base.

4. **Conclusion**:
Among the given options, \( \text{F}^- \) (Fluoride ion) is the only species that qualifies as a hard base.

### Final Answer:
The hard base among the given options is **Fluorine minus (\( \text{F}^- \))**.

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