Identify the process to which the following reaction belongs
`Al_(2) O_(3).2H_(2)O +Na_(2)CO_(3) rarr 2NaAlO_(2) +2H_(2)O +CO_(2)`
`2NaAlO_(2) +2H_(2)O +CO_(2) overset(50-60^(@)C)rarr Al_(2)O_(3).2H_(2)O +Na_(2)CO_(3)`

Options

A. Hall's process
B. Baeyer's process
C. Serpeck's process
D. None of these

Explanation

To identify the process to which the given reactions belong, we can follow these steps:

### Step 1: Analyze the Reactions
The first reaction is:
\[ \text{Al}_2\text{O}_3 \cdot 2\text{H}_2\text{O} + \text{Na}_2\text{CO}_3 \rightarrow 2\text{NaAlO}_2 + 2\text{H}_2\text{O} + \text{CO}_2 \]

In this reaction, aluminum hydroxide (bauxite) reacts with sodium carbonate to form sodium aluminate, water, and carbon dioxide.

The second reaction is:
\[ 2\text{NaAlO}_2 + 2\text{H}_2\text{O} + \text{CO}_2 \overset{50-60^\circ C}{\rightarrow} \text{Al}_2\text{O}_3 \cdot 2\text{H}_2\text{O} + \text{Na}_2\text{CO}_3 \]

In this reaction, sodium aluminate reacts with water and carbon dioxide at elevated temperatures to regenerate aluminum hydroxide and sodium carbonate.

### Step 2: Identify the Process
The reactions involve the extraction and regeneration of aluminum compounds, specifically from bauxite. This is characteristic of the Hall-Héroult process, which is used for the extraction of aluminum from its ores.

### Step 3: Conclusion
Thus, the process to which these reactions belong is the **Hall's process**, also known as the Hall-Héroult process, which is used for the extraction of aluminum from bauxite.

### Final Answer
The reactions belong to the **Hall's process**.

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