The correct statement is

Options

A. leaching of bauxite using concentrated `NaOH` solution gives sodium aluminate and sodium silicate
B. the blistered apperance of copper during the metallurgical process is due to the evoluation of `CO_(2)`
C. pig iron is obtained from cast iron
D. the Hall - Heroult process is used for the production of aluminium and iron

Answer

To solve the question, we will analyze each statement provided and determine its correctness based on our knowledge of chemistry.

### Step-by-Step Solution:

1. **Analyze the First Statement:**
- The statement claims that leaching of bauxite using concentrated NaOH solution gives sodium aluminate and sodium silicate.
- **Chemical Reaction:**
\[ \text{Al}_2\text{O}_3 + 2 \text{NaOH} + 3 \text{H}_2\text{O} \rightarrow 2 \text{NaAl(OH)}_4 + \text{Na}_2\text{SiO}_3 \]
- Here, bauxite (Al₂O₃) reacts with NaOH and water to produce sodium aluminate (NaAl(OH)₄) and sodium silicate (Na₂SiO₃).
- **Conclusion:** The first statement is correct.

2. **Analyze the Second Statement:**
- The statement claims that the blistered appearance of copper during the metallurgy process is due to the evolution of CO₂.
- **Chemical Reaction:**
\[ \text{Cu}_2\text{S} + 2 \text{Cu}_2\text{O} \rightarrow 6 \text{Cu} + \text{SO}_2 \]
- The blistering is due to the evolution of sulfur dioxide (SO₂), not carbon dioxide (CO₂).
- **Conclusion:** The second statement is incorrect.

3. **Analyze the Third Statement:**
- The statement claims that pig iron is obtained from cast iron.
- **Explanation:**
- Pig iron is produced from iron ore and has a higher carbon content (around 4%), while cast iron is derived from pig iron and has a lower carbon content (around 2-3%).
- **Conclusion:** The third statement is incorrect.

4. **Analyze the Fourth Statement:**
- The statement claims that the Hall-Heroult process is used for the production of aluminum and iron.
- **Explanation:**
- The Hall-Heroult process is specifically used for the extraction of aluminum from bauxite, not iron.
- **Conclusion:** The fourth statement is incorrect.

### Final Conclusion:
After analyzing all the statements, we find that only the first statement is correct. Therefore, the correct answer is **Option A**.