Which of the following statements are correct ?

Options

A. Fullerenes have dangling bonds
B. Fullerenes are cage-like molecules
C. Graphite is thermodynamically most stable allotrope of carbon
D. Graphite is slippery and hard and therefore used as a dry lubriant in machines

Explanation

To determine which statements are correct regarding fullerenes and graphite, we need to analyze each statement provided in the question.

### Step-by-Step Solution:

1. **Understanding Fullerenes:**
- Fullerenes are a form of carbon that can exist in various structures, most notably as C60, which resembles a soccer ball (a truncated icosahedron).
- They are indeed cage-like molecules, composed of carbon atoms arranged in a spherical shape.

2. **Dangling Bonds in Fullerenes:**
- The statement "Fullerenes have dangling bonds" is not entirely accurate. Fullerenes are stable structures with no dangling bonds in their most common forms (like C60). However, certain derivatives or reactions may involve reactive sites.

3. **Stability of Graphite:**
- Graphite is known to be the most thermodynamically stable allotrope of carbon under standard conditions. This statement is correct.

4. **Properties of Graphite:**
- Graphite is slippery due to its layered structure, which allows the layers to slide over each other easily. This property makes it useful as a dry lubricant. This statement is also correct.

5. **Thermodynamic Values:**
- The values mentioned in the statements related to enthalpy (like 1.98 kJ/mol or 38.1 kJ/mol) are not standard or widely recognized values associated with fullerenes or graphite. Therefore, these statements cannot be validated without proper context or references.

### Summary of Correct Statements:
- Fullerenes are cage-like molecules.
- Graphite is thermodynamically the most stable allotrope of carbon.
- Graphite is slippery and hard, making it useful as a dry lubricant.

### Final Answer:
The correct statements are:
- Fullerenes are cage-like molecules.
- Graphite is thermodynamically the most stable allotrope of carbon.
- Graphite is slippery and hard, making it useful as a dry lubricant.