In Hall process, in the production of A1, caebon is used as the anode material . The reaction are :

Options

A. Anode : `A1^(3+) + 3e^(-)rightaorrow A1`
cathod:
`C(s)+ 20^(2-) rightarrow CO_(2) (g)+ 4e^(-)`
B. Anode: `C_(s)+O_(2)rightarrow CO_(2)`
Cathod : `A1^(3+) + 3e^(-)rightarrowA1`
C. Anode : `A1rightarrow A1^(3+)+e^(-)`
Cathod : `Co_(2)+4e^(-)rightarrow C(s) + 2o^2-)`
D. None of above

Explanation

To solve the question regarding the Hall process in the production of aluminum, we will outline the key reactions that take place during the electrolysis of aluminum oxide (Al₂O₃) using carbon as the anode material.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- The Hall process involves the electrolysis of aluminum oxide (Al₂O₃) dissolved in a molten electrolyte, typically a mixture of cryolite (Na₃AlF₆) and aluminum fluoride (AlF₃).
- Carbon electrodes are used, where the anode is made of carbon and the cathode is typically a carbon lining of the cell.

2. **Electrolyte Preparation**:
- The aluminum oxide (Al₂O₃) is mixed with the electrolyte (cryolite and aluminum fluoride) to lower its melting point and increase conductivity.

3. **Electrolysis Reaction**:
- When electricity is passed through the molten electrolyte, aluminum ions (Al³⁺) migrate to the cathode, and oxide ions (O²⁻) migrate to the anode.
- The reactions at the electrodes can be summarized as follows:

**At the Cathode (Reduction)**:
\[ \text{Al}^{3+} + 3e^- \rightarrow \text{Al} (l) \]
- Aluminum ions gain electrons (reduction) to form liquid aluminum.

**At the Anode (Oxidation)**:
\[ 2\text{O}^{2-} \rightarrow \text{O}_2 (g) + 4e^- \]
- Oxide ions lose electrons (oxidation) to form oxygen gas.

4. **Reaction of Oxygen with Carbon**:
- The oxygen produced at the anode reacts with the carbon anode to form carbon monoxide (CO) or carbon dioxide (CO₂):
\[ \text{C} + \text{O}_2 \rightarrow \text{CO}_2 (g) \]
or
\[ 2\text{C} + \text{O}_2 \rightarrow 2\text{CO} (g) \]

5. **Overall Reaction**:
- The overall reaction for the Hall process can be summarized as:
\[ 2\text{Al}_2\text{O}_3 (l) \rightarrow 4\text{Al} (l) + 3\text{O}_2 (g) \]
- This indicates that aluminum is produced while oxygen is released as a byproduct.

### Summary of Reactions:
- **At Cathode**:
\[ \text{Al}^{3+} + 3e^- \rightarrow \text{Al} (l) \]
- **At Anode**:
\[ 2\text{O}^{2-} \rightarrow \text{O}_2 (g) + 4e^- \]
- **Carbon Reaction**:
\[ \text{C} + \text{O}_2 \rightarrow \text{CO}_2 (g) \]
or
\[ 2\text{C} + \text{O}_2 \rightarrow 2\text{CO} (g) \]