Carbon cannot be used in the reduction of `A1_(2)O_(3)` because:

Options

A. it is non-metal
B. the heat of formation of `CO_(2)` is more than that of `Al_(2)O_(3)`
C. pure carbon is not easily available
D. the heat of formation of `Al_(2)O_(3)` is too high

Answer

To solve the question of why carbon cannot be used in the reduction of Al₂O₃, we will analyze the options provided and identify the correct reasoning step by step.

### Step-by-Step Solution:

1. **Understanding the Reduction Process**:
- The reduction of Al₂O₃ (alumina) to aluminum involves removing oxygen from the compound. This process requires a reducing agent.

2. **Evaluating the Options**:
- **Option 1**: Carbon is a non-metal.
- While carbon is indeed a non-metal, this does not inherently prevent it from being used as a reducing agent. Non-metals can sometimes act as reducing agents depending on the reaction conditions.

- **Option 2**: The heat of formation of CO₂ is more than that of Al₂O₃.
- This statement is misleading. The heat of formation of CO₂ being higher does not directly relate to the feasibility of using carbon for the reduction of Al₂O₃.

- **Option 3**: Pure carbon is not easily available.
- This is not a valid reason in the context of chemical reactions. Carbon is generally available in various forms (like coke or charcoal) for industrial processes.

- **Option 4**: The heat of formation of Al₂O₃ is too high.
- This is the most relevant point. The enthalpy of formation of Al₂O₃ is indeed very high, which means that a significant amount of energy is required to break the bonds in Al₂O₃ to reduce it to aluminum. Carbon does not provide sufficient energy to overcome this high enthalpy barrier.

3. **Conclusion**:
- Based on the analysis, the correct reason why carbon cannot be used in the reduction of Al₂O₃ is **Option 4**: the heat of formation of Al₂O₃ is too high.

### Final Answer:
Carbon cannot be used in the reduction of Al₂O₃ because the heat of formation of Al₂O₃ is too high.