The correct statement is :

Options

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

Explanation

To solve the question, we need to analyze each statement provided in the options and determine which one is correct. Let's go through each statement step by step.

### Step-by-Step Solution:

1. **Analyze the First Statement:**
- The statement claims that the Hall-Héroult process is used for the production of aluminum and iron.
- The Hall-Héroult process is specifically an electrolysis process used to extract aluminum from alumina (Al₂O₃).
- It is not used for the production of iron.
- **Conclusion:** This statement is **not correct**.

2. **Analyze the Second Statement:**
- The statement claims that leaching of bauxite using concentrated sodium hydroxide solution gives sodium aluminate and sodium silicate.
- During the leaching process, bauxite (which contains aluminum oxide) is treated with concentrated sodium hydroxide at high temperatures (473 K to 573 K).
- The reaction can be represented as:
\[ \text{Al}_2\text{O}_3 + 2\text{NaOH} + 3\text{H}_2\text{O} \rightarrow 2\text{NaAl(OH)}_4 \]
- Additionally, silica (SiO₂) present in bauxite reacts with sodium hydroxide to form sodium silicate.
- **Conclusion:** This statement is **correct**.

3. **Analyze the Third Statement:**
- The statement claims that the blistered appearance of copper during the metallurgical process is due to the evolution of carbon dioxide.
- The blistered appearance of copper is actually due to the evolution of sulfur dioxide (SO₂) gas during the reduction of copper ores.
- The relevant reaction is:
\[ 2\text{Cu}_2\text{O} + \text{Cu}_2\text{S} \rightarrow 6\text{Cu} + \text{SO}_2 \]
- **Conclusion:** This statement is **not correct**.

4. **Analyze the Fourth Statement:**
- The statement claims that pig iron is obtained from cast iron.
- Pig iron is produced in a blast furnace and contains about 4% carbon and various impurities.
- Cast iron is made by melting pig iron with scrap iron and coke in the presence of hot air.
- Therefore, pig iron is not obtained from cast iron; rather, cast iron is derived from pig iron.
- **Conclusion:** This statement is **not correct**.

### Final Conclusion:
The only correct statement among the options is the **second statement**: "Leaching of bauxite using concentrated sodium hydroxide solution gives sodium aluminate and sodium silicate."