Which of the following is a hard acid ?

Options

A. `Br_2`
B. `Cd^(2 +)`
C. `CO_2`
D. `Fe^(3 +)`

Answer

To determine which of the given options is a hard acid, we need to understand the characteristics of hard acids. Hard acids are typically metal ions that possess the following properties:

1. **High Positive Charge**: Hard acids usually have a high positive oxidation state.
2. **Small Size**: They are generally small in size, which allows them to have a strong interaction with hard bases.
3. **Low Polarizability**: Hard acids are not easily polarizable, meaning their electron clouds do not distort easily.

Now, let's analyze the given options:

1. **Bromine (Br)**: This is a non-metal and does not fit the criteria for a hard acid.
2. **Cadmium (Cd²⁺)**: Cadmium is a transition metal, but it has a relatively low charge density compared to other transition metals and is more polarizable, making it less likely to be classified as a hard acid.
3. **Carbon Dioxide (CO₂)**: While carbon can be considered to have a high electronegativity, CO₂ is generally not classified as a hard acid in the context of Lewis acid-base theory.
4. **Iron (Fe³⁺)**: Iron in the +3 oxidation state is a transition metal with a high positive charge and a relatively small ionic radius, which makes it a hard acid.

Based on this analysis, we can conclude that the hard acids from the options provided are:

- **Iron (Fe³⁺)**

Thus, the answer is **Iron (Fe³⁺)**.

### Step-by-Step Solution:
1. **Identify the properties of hard acids**: High positive charge, small size, low polarizability.
2. **Analyze each option**:
- **Bromine**: Non-metal, not a hard acid.
- **Cadmium (Cd²⁺)**: Transition metal but more polarizable, not a hard acid.
- **Carbon Dioxide (CO₂)**: Not classified as a hard acid.
- **Iron (Fe³⁺)**: Transition metal, high positive charge, small size, qualifies as a hard acid.
3. **Conclusion**: The hard acid among the options is **Iron (Fe³⁺)**.