Which of the following is the correct order of stability of allotropes of carbon?

Options

A. `"Diamond" lt" graphite"lt"fullerene"`
B. `"Fullerene"lt"graphite"lt"diamond"`
C. `"Graphite"lt"fullerene"lt"diamond"`
D. `"Fullerene"lt"diamond"lt"graphite"`

Answer

To determine the correct order of stability of the allotropes of carbon, we need to analyze the stability of each allotrope based on their structures and properties. The main allotropes of carbon we will consider are fullerenes, diamond, and graphite.

### Step-by-Step Solution:

1. **Identify the Allotropes of Carbon**:
- The primary allotropes of carbon are:
- Fullerenes (e.g., C60)
- Diamond
- Graphite

2. **Analyze the Structure of Each Allotrope**:
- **Fullerenes**: These are spherical structures made up of carbon atoms arranged in pentagons and hexagons. They are known to be highly strained due to the presence of five-membered rings, which makes them less stable.
- **Diamond**: Diamond has a tetrahedral structure where each carbon atom is bonded to four other carbon atoms in a three-dimensional network. This strong covalent bonding makes diamond very hard and stable.
- **Graphite**: Graphite consists of layers of carbon atoms arranged in hexagonal lattices. Each carbon atom is bonded to three others, and there is a delocalized electron in each layer, allowing for conductivity. Graphite has a lower enthalpy of formation compared to diamond, indicating greater stability.

3. **Determine the Stability Based on Enthalpy**:
- Stability can be assessed by looking at the enthalpy of formation. The more negative the enthalpy of formation, the more stable the allotrope.
- Graphite has the most negative enthalpy of formation, making it the most stable allotrope of carbon.
- Diamond, while very hard and strong, has a less negative enthalpy of formation compared to graphite, thus it is less stable than graphite.
- Fullerenes, due to their strained structures, have the least stability.

4. **Establish the Order of Stability**:
- Based on the analysis:
- Most stable: Graphite
- Less stable: Diamond
- Least stable: Fullerenes

5. **Final Conclusion**:
- The correct order of stability of the allotropes of carbon is:
- Graphite > Diamond > Fullerenes